How can I solve the simultaneous equations: x51+x52=464, x1+x2=4 ?

Answer 1

x⁵¹ + x⁵² = 464 = x⁵⁰(x + x²)

As long as x + x² ≠ 0, divide this equation by the other given equation to get x⁵⁰ = 116.

Your calculator will extract this root for you or you can use logarithms to solve it.

Answer 2

Given:

x⁵¹ + x⁵² = 464, x¹ + x² = 4

Solving:

x⁵¹ + x⁵² = 464

x⁵⁰ (x¹ + x²) = 464 [factored out x⁵⁰ on the left side of the equation]

x⁵⁰ ( 4 ) = 464 [substituted since we're given x¹ + x² = 4]

x⁵⁰ = 116 [divided by 4 on both sides]

x = 116^1/50 [raised both sides to the 1/50th power]

≈ 1.0997